What makes a record collection "great"?

Good question.
But like the others, it's what moves you that matters. Sometimes that same LP will have a profound effect on a friend, or young audiophile to-be.
I have about 1200 LPs.
There are a few gems which really do it for me and I tend to play certain records for a specific mood.
Classical: maybe my favorite Mozart Quartet, or Bach LP.
Jazz: could be Herb Ellis and Joe Pass on guitars. Or Coltrane, Miles.
Swing and dance: Bob Wills
Rock: Stones, Los Lobos, The Clash
But there are many others which lead me to and from the few which remain in circulation.

A great record is one that moves YOU.
The more records you have that move YOU the greater the collection.

I like Jwong thoughts about a great collection in book terms. I do not own many 1st pressings except those that I bought back in the day. Not sure my collection would classify as great. But it has a slant on music that is tailored to my taste and so as others has said that makes it great to me. Along with my USA pressings, i do have a handful of english, german and Japanese pressing that do sound very good as well as a small group of mofi/nautilus records. But what makes it special to me is the fact that i listen to them. I have a friend that has a collection of several hundred with many being 1st pressings or rarities. He has not owned a table in 15 years. (yeah such a crime). But his collection is worth far more money than mine because of his selections based on rarity and cover condition vs a musical theme. Whos collection is greatest. Mine of course:^)

It depends on the view
What is great?
A collection of reissues?
A collection from church Music 16th Century?
A collection from RCA Living Stereos? What stampers?
Great is normally rated from others, it is a definition how they like it or the thinking about it's price (now or in future).
Supply and demand
Private opinions are taste only. When I like my 15000$ Rap and Hip hop records (which I don't have) and my visitors start to cry when I do a demo, well, then I am alone with my "Great Collection". But for me it is still great.

Btw. same with Stereo systems and their owners...
or cars.... =)

My collection is great because it is special to me. Many of the titles take me back to junior high, my first crush, prom-night, first love, Sundays after church listening to my parents Big Band, Swing and Jazz collection before dinner. All the important times and memories of our life can likely be relived in some small way by hearing that "one" song or album whose music floods our senses with the sounds we remember. It allows us to experience again in the imagination those days gone by. Who can remember where they were the first time the heard Etta, Ella, Elvis, Janis, Jimmy, Bob (Dylan, Marley,) The Beach Boys, Carol King, Michael J. Etc. My collection spans the 40's-- late 1990's. Every important time of my life has several titles that I can reminisce with and I can find music for whatever mood I am in. It gives me a great amount of pleasure and puts a big smile on my face just thinking about it. A record collection that can do this for you is one that you can feel GREAT about!